\textit{Nothing on TV? Why not join us in a bar for a drink?} Message on TV program in one London hote John likes going to London pubs. Unfortunately there is no pub directly in a house he lives, but there are plenty around. John like going to pubs, but it is not any pub that he would go. When going to a pub, John often thinks that he is going to a wrong pub and he should go to another one. Recently John has met his friend, psychologist and mathematician Jack and told him about his problem. They made an investigation and found out when John thinks that he is going to the wrong pub. Consider pubs as points on a plane, let John's home be located at point (\textbf{0}, \textbf{0}) and pubs be located at points (\textbf{x_i}, \textbf{y_i}). Consider the \textbf{i}-th pub located at (\textbf{x_i}, \textbf{y_i}), draw a circle with segment (\textbf{0},\textbf{ 0})-(\textbf{x}_i,\textbf{ y}_i) as a diameter. Let us call such pub \textit{good} if there is no other good pub located inside this circle or on its border. John is feeling good only when he is going to a good pub. Now John and Jack wonder, what are the pubs that John could go without feeling being wrong. Help them! \InputFile The first line of the input file contains \textbf{n} the number of pubs in John's neighborhood (\textbf{1} ≤ \textbf{n} ≤ \textbf{100000}). The following\textbf{n} lines contain two integer numbers \textbf{x_i} and \textbf{y_i} each (|\textbf{x_i}|, |\textbf{y_i}| ≤ \textbf{30000}). No two pubs coincide. There is no pub at (\textbf{0}, \textbf{0}). \OutputFile The first line of the output file must contain \textbf{k} - the number of good pubs. The second line must contain \textbf{k} integer numbers - the numbers of these pubs. Pubs are numbered starting from 1 in order they are listed in the input file. Note that there is a pub at (\textbf{1}, \textbf{1}) inside the circle for pub at (\textbf{-1}, \textbf{4}), but that pub is not good, so it's not important.